Developing precise computational models of bone remodeling can lead to more successful types of orthopedic treatments and deeper understanding of the phenomenon. Empirical evidence has shown that bone adaptation to mechanical loading is frequency dependent, and the modal behavior of bone under vibration can play a significant role in remodeling process, particularly in the resonance region. The objective of this study is to develop a bone remodeling algorithm that takes into account the effects of bone vibrational behavior. An extended/modified model is presented based on conventional finite element (FE) remodeling models. Frequency domain analysis is used to introduce appropriate correction coefficients to incorporate the effect of bone's frequency response (FR) into the model. The method is implemented on a bovine bone with known modal/vibration characteristics. The rate and locations of new bone formation depend on the loading frequency and are consistently correlated with the bone modal behavior. Results show that the proposed method can successfully integrate the bone vibration conditions and characteristics with the remodeling process. The results obtained support experimental observations in the literature.
Issue Section:
Research Papers
References
1.
Beaupre
, G. S.
, Orr
, T. E.
, and Carter
, D. R.
, 1990
, “An Approach for Time Dependent Bone Modeling and Remodeling—Theoretical Development
,” J. Orthop. Res.
, 8
(5
), pp. 651
–661
.2.
Lerch
, M.
, Kurtz
, A.
, Stukenborg-Colsman
, C.
, Nolte
, I.
, Weigel
, N.
, Bouguecha
, A.
, and Behrens
, B. A.
, 2012
, “Bone Remodeling After Total Hip Arthroplasty With a Short Stemmed Metaphyseal Loading Implant: Finite Element Analysis Validated by a Prospective DEXA Investigation
,” J. Orthop. Res.
, 30
(11
), pp. 1822
–1829
.3.
Thompson
, W. R.
, Yen
, S. S.
, and Rubin
, J.
, 2014
, “Vibration Therapy: Clinical Applications in Bone
,” Curr. Opin. Endocrinol. Diabetes Obes.
, 21
(6
), pp. 447
–453
.4.
Ghiasi
, M. S.
, Chen
, J.
, Vaziri
, A.
, Rodriguez
, E. K.
, and Nazarian
, A.
, 2017
, “Bone Fracture Healing in Mechanobiological Modeling: A Review of Principles and Methods
,” Bone Rep.
, 6
, pp. 87
–100
.5.
Cowin
, S. C.
, and Van Buskirk
, W. C.
, 1979
, “Surface Bone Remodeling Induced by a Medullary Pin
,” J. Biomech.
, 12
(4
), pp. 269
–276
.6.
Jang
, I. G.
, and Kim
, I. Y.
, 2010
, “Computational Simulation of Simultaneous Cortical and Trabecular Bone Change in Human Proximal Femur During Bone Remodeling
,” J. Biomech.
, 43
(2
), pp. 294
–301
.7.
Pettermann
, H. E.
, Reiter
, T. J.
, and Rammerstorfer
, F. G.
, 1997
, “Computational Simulation of Internal Bone Remodeling
,” Arch. Comput. Methods Eng.
, 4
(4
), pp. 295
–323
.8.
Pereira
, A. F.
, Javaheri
, B.
, Pitsillides
, A. A.
, and Shefelbine
, S. J.
, 2015
, “Predicting Cortical Bone Adaptation to Axial Loading in the Mouse Tibia
,” J. R. Soc. Interface
, 12
(110
), pp. 1–14.9.
Oftadeh
, R.
, Perez-Viloria
, M.
, Villa-Camacho
, J. C.
, Vaziri
, A.
, and Nazarian
, A.
, 2015
, “Biomechanics and Mechanobiology of Trabecular Bone: A Review
,” ASME J. Biomech. Eng.
, 137
(1
), p. 10802
.10.
Ozcivici
, E.
, Luu
, Y. K.
, Adler
, B.
, Qin
, Y.-X.
, Rubin
, J.
, Judex
, S.
, and Rubin
, C. T.
, 2010
, “Mechanical Signals as Anabolic Agents in Bone
,” Nat. Rev. Rheumatol.
, 6
(1
), pp. 50
–59
.11.
Frost
, H. M.
, 1990
, “Skeletal Structural Adaptations to Mechanical Usage (SATMU)—Part 1: Redefining Wolff's Law: The Bone Modeling Problem
,” Anat. Rec.
, 226
(4
), pp. 403
–413
.12.
Carter
, D. R.
, Fyhrie
, D. P.
, and Whalen
, R. T.
, 1987
, “Trabecular Bone Density and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy
,” J. Biomech.
, 20
(8
), pp. 785
–794
.13.
Kourtis
, L. C.
, Carter
, D. R.
, Kesari
, H.
, and Beaupre
, G. S.
, 2008
, “A New Software Tool (VA-BATTS) to Calculate Bending, Axial, Torsional and Transverse Shear Stresses Within Bone Cross Sections Having Inhomogeneous Material Properties
,” Comput. Methods Biomech. Biomed. Eng.
, 11
(5
), pp. 463
–476
.14.
Marzban
, A.
, Canavan
, P.
, Warner
, G.
, Vaziri
, A.
, and Nayeb-Hashimi
, H.
, 2012
, “Parametric Investigation of Load-Induced Structure Remodeling in the Proximal Femur
,” Proc. Inst. Mech. Eng. Part H: J. Eng. Med.
, 226
(6
), pp. 450
–460
.15.
Huiskes
, R.
, Weinans
, H.
, Grootenboer
, H. J.
, Dalstra
, M.
, Fudala
, B.
, and Slooff
, T. J.
, 1987
, “Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis
,” J. Biomech.
, 20
(11–12
), pp. 1135
–1150
.16.
Jang
, I. G.
, and Kim
, I. Y.
, 2008
, “Computational Study of Wolff's Law With Trabecular Architecture in the Human Proximal Femur Using Topology Optimization
,” J. Biomech.
, 41
(11
), pp. 2353
–2361
.17.
Coelho
, P. G.
, Rodrigues
, H. C.
, and Fernandes
, P. R.
, 2008
, “Bone Tissue Adaptation—A Hierarchical Approach for Apparent Density and Trabecular Structure
,” J. Biomech.
, 41
(S1), p. S125
.18.
Sadegh
, A. M.
, Luo
, G. M.
, and Cowin
, S. C.
, 1993
, “Bone Ingrowth: An Application of the Boundary Element Method to Bone Remodeling at the Implant Interface
,” J. Biomech.
, 26
(2
), pp. 167
–182
.19.
Viceconti
, M.
, Ricci
, S.
, Pancanti
, A.
, and Cappello
, A.
, 2004
, “Numerical Model to Predict the Longterm Mechanical Stability of Cementless Orthopaedic Implants
,” Med. Biol. Eng. Comput.
, 42
(6
), pp. 747
–753
.20.
Hsieh
, Y.
, and Turner
, C. H.
, 2001
, “Effects of Loading Frequency on Mechanically Induced Bone Formation
,” J. Bone Miner. Res.
, 16
(5
), pp. 918
–924
.21.
Warden
, S. J.
, and Turner
, C. H.
, 2004
, “Mechanotransduction in the Cortical Bone Is Most Efficient at Loading Frequencies of 5–10 Hz
,” Bone
, 34
(2
), pp. 261
–270
.22.
Kameo
, Y.
, Adachi
, T.
, and Hojo
, M.
, 2011
, “Effects of Loading Frequency on the Functional Adaptation of Trabeculae Predicted by Bone Remodeling Simulation
,” J. Mech. Behav. Biomed. Mater.
, 4
(6
), pp. 900
–908
.23.
Tanaka
, S. M.
, Alam
, I. M.
, and Turner
, C. H.
, 2003
, “Stochastic Resonance in Osteogenic Response to Mechanical Loading
,” Faseb J.
, 17
(2
), pp. 313
–314
.24.
Zhao
, L.
, Dodge
, T.
, Nemani
, A.
, and Yokota
, H.
, 2014
, “Resonance in the Mouse Tibia as a Predictor of Frequencies and Locations of Loading-Induced Bone Formation
,” Biomech. Model. Mechanobiol.
, 13
(1
), pp. 141
–151
.25.
Zhang
, P.
, Tanaka
, S. M.
, Sun
, Q.
, Turner
, C. H.
, and Yokota
, H.
, 2007
, “Frequency-Dependent Enhancement of Bone Formation in Murine Tibiae and Femora With Knee Loading
,” J. Bone Miner. Metab.
, 25
(6
), pp. 383
–391
.26.
Han
, Z. H.
, Palnitkar
, S.
, Rao
, D. S.
, Nelson
, D.
, and Parfitt
, M.
, 1997
, “Effects of Ethnicity and Age or Menopause on the Remodeling and Turnover of Iliac Bone
,” J. Bone Min. Res.
, 12
(4
), pp. 498
–508
.27.
Fares
, J. E.
, Choucair
, M.
, Nabulsi
, M.
, Salamoun
, M.
, Shahine
, C. H.
, and Fuleihan
, G. E. H.
, 2003
, “Effect of Gender, Puberty, and Vitamin D Status on Biochemical Markers of Bone Remodedeling
,” Bone
, 33
(2
), pp. 242
–247
.28.
Weinans
, H.
, Huiskes
, R.
, and Grootenboer
, H. J.
, 1992
, “The Behavior of Adaptive Bone-Remodeling Simulation Models
,” J. Biomech.
, 25
(12
), pp. 1425
–1441
.29.
Moghaddam
, A. O.
, Mahjoob
, M. J.
, and Nazarian
, A.
, 2016
, “Assigning Material Properties to Finite Element Models of Bone: A New Approach Based on Dynamic Behavior
,” 7th International Conference on Computational Methods (ICCM
), Berkeley, CA, Aug. 1–4, pp. 1
–9
.http://www.sci-en-tech.com/ICCM2016/PDFs/1759-6308-1-PB.pdf30.
Wagner
, D. W.
, Divringi
, K.
, Ozcan
, C.
, Grujicic
, M.
, Pandurangan
, B.
, and Grujicic
, A.
, 2010
, “Combined Musculoskeletal Dynamics/Structural Finite Element Analysis of Femur Physiological Loads During Walking
,” Multidiscip. Model. Mater. Struct.
, 6
(4
), pp. 417
–437
.31.
Erdemir
, A.
, McLean
, S.
, Herzog
, W.
, and van den Bogert
, A. J.
, 2007
, “Model-Based Estimation of Muscle Forces Exerted During Movements
,” Clin. Biomech.
, 22
(2
), pp. 131
–154
.32.
Turner
, C. H.
, and Robling
, A. G.
, 2003
, “Designing Exercise Regimens to Increase Bone Strength
,” Exercise Sport Sci. Rev.
, 31
(1
), pp. 45
–50
.33.
Zhang
, P.
, Malacinski
, G. M.
, and Yokota
, H.
, 2008
, “Joint Loading Modality: Its Application to Bone Formation and Fracture Healing
,” Br. J. Sports Med.
, 42
(7
), pp. 556
–560
.Copyright © 2018 by ASME
You do not currently have access to this content.
